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Drain to substrate current is an important parameter affecting loss, breakdown and reliability of power GaN HEMTs on Si substrates; however, no clear model of the current has been established. This work proposes a novel approach describing the drain to substrate current as a function of equivalent Si/GaN interface barrier. The modeling results are in close agreement with experimental observations; they reveal an important role of space charge injection from Si substrate into GaN buffer. Compact model closely reproducing experimental data is presented. The results are important for GaN on Si power switches development.

Peristaltic motions are used in a variety of industrial and real-world problems such as pumping mixture with such a high solid content from the mining sector, biogases, sewers facilities, food flow through the gastrointestinal system, urinary tract, and fallopian tube of human females where extremely abrasive, gritty, and viscous fluids are present. The goal of this theoretical study is to examine the impact of the lubricated walls on the peristaltic transport of a viscous fluid in an asymmetric medium. The interfacial condition is derived under the assumptions of thin film lubrication and long wavelength approximation. The theory of a dynamical system is utilized to examine the lubrication effects on the position and bifurcation of stagnation points in the flow. For this, three flow distributions, backward flow, trapping, and augmented flow, are discussed. The obtained system of equations is solved numerically by the shooting method based on Newton–Raphson root-finding algorithm in Mathematica. The prime findings for the velocity profile, pressure increase, trapping, and reflux criteria are illustrated through graphs. Bifurcation occurs earlier by increasing the influence of lubrication. The trapping area diminishes and the augmented flow section expands with the lubrication parameter. This will be useful for medical engineering, industrial and physiological systems. The comparison for the particular case of no-slip condition is presented and found to be in excellent agreement.

For the Bose-condensed gas in a one-dimensional optical lattice, several far-off resonant laser beams are used to split and trap the matter wavepacket after switching off both the magnetic trap and optical lattices. In the presence of two far-off resonant laser beams which are not symmetric about the centre of the matter wavepacket, we propose an experimental scheme to observe the collision between two side peaks after switching off the magnetic trap and optical lattice. We also discuss an experimental scheme to realize a coherent splitting and trapping of the matter wavepacket which has potential application in atom optics.

Recent findings suggest that processes such as the excitonic energy transfer through the photosynthetic antenna display quantal features, aspects known from the dynamics of charge carriers along polymer backbones. Hence, in modeling energy transfer one has to leave the classical, master-equation-type formalism and advance towards an increasingly quantum-mechanical picture, while still retaining a local description of the complex network of molecules involved in the transport, say through a tight-binding approach.

Interestingly, the continuous time random walk (CTRW) picture, widely employed in describing transport in random environments, can be mathematically reformulated to yield a quantum-mechanical Hamiltonian of tight-binding type; the procedure uses the mathematical analogies between time-evolution operators in statistical and in quantum mechanics: The result are continuous-time quantum walks (CTQWs). However, beyond these formal analogies, CTRWs and CTQWs display vastly different physical properties. In particular, here we focus on trapping processes on a ring and show, both analytically and numerically, that distinct configurations of traps (ranging from periodical to random) yield strongly different behaviors for the quantal mean survival probability, while classically (under ordered conditions) we always find an exponential decay at long times.

The phenomenon of synchronization (trapping) of coming waves by the resonant water area in a coastal zone of the sea found from the observed data is considered in the paper. Edge waves with the period of about 10.7 minutes are visually observed in sea level fluctuations near the village of Okhotskoye and the cape Ostri on the southeast coast of Sakhalin Island. These waves are synchronized with the resonance water area. It becomes apparent from the unlimited increase of a phase between the bottom stations installed at distance of about 7.5km. In relation to the phenomenon found, the problem of weak and periodic impact on regular self-oscillatory system — Van der Paul’s oscillator — is considered. Good compliance between theoretical model and data of experiments is obtained.

This paper deals with a theoretical investigation of the peristaltic transport of a physiological fluid in a porous asymmetric channel under the action of a magnetic field. The stream function, pressure gradient, and axial velocity are studied by using appropriate analytical and numerical techniques. Effects of different physical parameters such as permeability, phase difference, wave amplitude and magnetic parameter on the velocity, pumping characteristics, streamline pattern, and trapping are investigated with particular emphasis. The computational results are presented in graphical form. The results are found to be in perfect agreement with those of a previous study carried out for a nonporous channel in the absence of a magnetic field.

The paper deals with a theoretical investigation of the peristaltic transport of a couple stress fluid in a porous channel. The study is motivated toward investigating the physiological flow of blood in the micro-circulatory system, by taking account of the particle size effect. The velocity, pressure gradient, stream function, and frictional force of blood are investigated, when the Reynolds number is small and the wavelength is large, by using appropriate analytical and numerical methods. Effects of different physical parameters reflecting porosity, Darcy number, couple stress parameter, as well as amplitude ratio on velocity profiles, pumping action and frictional force, streamlines pattern, and trapping of blood are studied with particular emphasis. The computational results are presented in graphical form. The results are found to be in good agreement with those reported by Shapiro et al.⁵² that was carried out for a non-porous channel without consideration of couple stress effect. The present study puts forward an important observation that for peristaltic transport of a couple stress fluid during free pumping, flow reversal can be considerably controlled by suitably adjusting the couple stress effect of the fluid/Darcy permeability of the channel. It is also possible to avoid the occurrence of trapping, by reducing the permeability.

A mathematical model is developed to study the characteristics of blood flow through flexible inclined arteries under the influence of an inclined magnetic field. The blood is supposed to be couple stress fluid and the geometry of wall surface of inclined arteries is taken as peristaltic wave. The expressions for axial velocity, volume flow rate, pressure gradient and stream function are obtained under the assumptions of long wavelength and low Reynolds number. The effects of different physical parameters reflecting couple stress parameter, Hartmann number, Reynolds number, Froude number, inclination of channel and inclination of magnetic field on velocity profile, pressure and frictional force are discussed. The stream lines are drawn for various values of emerging parameters and the trapping phenomenon is discussed. The significant features of the blood flow characteristics are analyzed by plotting graphs and discussed numerically in detail.

This article studies the hydromagnetic peristaltic flow of couple stress fluids through the gap between two concentric channels containing a Darcian porous medium, with the inner channel being rigid. A sinusoidal wave propagates along the outer channel. Long wavelength and low Reynolds number assumptions are used. The effects of couple stress parameter, magnetic field, permeability, and the channel ratio width on pressure and frictional forces on the inner and outer channels are depicted graphically. Mechanical efficiency and trapping are also studied. Pressure diminishes with increasing coupling and permeability parameters whereas it increases with Hartmann number and channel width ratio. Applications of the model include transport of complex bio-waste fluids and magnetic field control of gastro-intestinal disorders.

A mathematical model is developed to analyze electro-kinetic effects on unsteady peristaltic transport of blood in cylindrical vessels of finite length. The Newtonian viscous model is adopted. The analysis is restricted under Debye–Hückel linearization (i.e., wall zeta potential $\le$ 25mV) is sufficiently small). The transformed, nondimensional conservation equations are derived via lubrication theory and long wavelength and the resulting linearized boundary value problem is solved exactly. The case of a thin electric double layer (i.e., where only slip electro-osmotic velocity considered) is retrieved as a particular case of the present model. The response in pumping characteristics (axial velocity, pressure gradient or difference, volumetric flow rate, local wall shear stress) to the influence of electro-osmotic effect (inverse Debye length) and Helmholtz–Smoluchowski velocity is elaborated in detail. Visualization of trapping phenomenon is also included and the bolus dynamics evolution with electro-kinetic effects examined. A comparative study of train wave propagation and single wave propagation is presented under the effects of thickness of EDL and external electric field. The study is relevant to electrophoresis in haemotology, electrohydrodynamic therapy and biomimetic electro-osmotic pumps.

A precise model is presented to designate the curvature effects in electroosmotic flow classifications to organize flow in a curved micro-vessel. Heat transfer analysis is also considered under the viscous dissipation effect. Lubrication scheme, Debye–Hückel estimation, and suitable boundary conditions have been employed to arising nonlinear system. The coupled nonlinear PDEs are solved numerically using Mathematica software. The obtained numerical results for electric potential, stream function, pressure gradient, axial velocity, temperature and shear stress are displayed through graphical illustrations. Trapping for blood flow under the effects of physical parameter is also discussed. The annotations also demonstrate the silent features of the micro-mixer peristaltic pumps and chip devices which may additionally be exploited in hemodialysis and judgement of samples respectively.

Granular surface flows have still to be fully modelled. Here, we present the four types of front that can be observed in avalanches. These strongly inhomogeneous and unsteady flows are very sensitive test cases for the different types of model. We show that, at least qualitatively for the moment, the model we propose, based on the analysis of the motion of a single grain and layers of grains, can reproduce the different characteristics of these four fronts.

Based on the linear long wave theory, analytical solutions are obtained for the propagation of tsunamis with an arbitrary incident wave profile around a conical island. The validity of the theory is verified through comparisons with two laboratory datasets. Effects of incident wave profile on the distribution of runup height and on the maximum runup height along the coastline of an island are discussed on the basis of this theory.

Based on the linear long wave theory, a theoretical solution is obtained for the transient tsunamis propagating into a conical island having a vertical wall around its coastline. The solutions are compared with the numerical solutions obtained by the Leap-Frog finite difference method using a staggered grid system to examine the relationship between the grid size and the accuracy of numerical simulation. The comparison reveals that Aida's parameter, which is a representative to evaluate the numerical error, is represented by the function of the simple parameter, . The criterion for grid size selection is determined, once the required numerical accuracy is set for the prediction of the maximum tsunami height and so on.

Based on the linear long wave theory, a theoretical solution was obtained for the tsunami, which propagated from a tsunami source generated on the shelf with a straight coastline and a uniform slope. The solution shows that the behavior of a tsunami generated on the shelf is affected by the conditions of the tsunami source. The tsunami propagation is classified into three types by examining the generated edge waves. The limit of conditions providing each propagation type is determined mainly by the source distance to the coastline. The empirical relations are derived which evaluate the characteristics of induced tsunami by using the tsunami source parameters such as the lengths of the long-axis and short-axis, the location and the direction of the tsunami source and so on. The effect of the Coriolis force is also discussed.

Peristaltic transport of an incompressible couple stress fluid in a two-dimensional uniform channel with wall effects and in the presence of magnetic field has been studied. Using long wavelength approximation with low Reynolds number and dynamic boundary conditions, analytical expressions have been derived for velocity and stream function and the effects of pertinent parameters on these flow variables have been studied. The numerical results show that the time average velocity decreases with viscous damping force. Further, it has been observed that trapping occurs and the size of the trapped bolus decreases with Hartman number.

Granular surface flows have still to be fully modelled. Here, we present the four types of front that can be observed in avalanches. These strongly inhomogeneous and unsteady flows are very sensitive test cases for the different types of model. We show that, at least qualitatively for the moment, the model we propose, based on the analysis of the motion of a single grain and layers of grains, can reproduce the different characteristics of these four fronts.

Drain to substrate current is an important parameter affecting loss, breakdown and reliability of power GaN HEMTs on Si substrates; however, no clear model of the current has been established. This work proposes a novel approach describing the drain to substrate current as a function of equivalent Si/GaN interface barrier. The modeling results are in close agreement with experimental observations; they reveal an important role of space charge injection from Si substrate into GaN buffer. Compact model closely reproducing experimental data is presented. The results are important for GaN on Si power switches development.